$2$
$2\sqrt { 6 }$
$3$
$\sqrt { 6 }$
$2\sqrt { 2 }$
$2\sqrt { 3 }$

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Let $r , R_1 , R_2$ be the radius of the inner circle, middle and outer circle respectively.

Then according to the question:

$\large \displaystyle \pi (R_1^2 - r^2) = \pi r^2\\ \large \displaystyle R_1^2 - 3 = 3 \implies R_1 = \sqrt6.$

$\large \displaystyle \pi (R_2^2 - R_1^2) = \pi r^2\\ \large \displaystyle R_2^2 - 6 = 3 \implies R_2 = 3.$

$\large \displaystyle \therefore \text{The radius of the largest circle is } \color{#D61F06}{\boxed{3}}.$